Percolation, fractals and the critical point in a nuclear reactor

Abstract

The trajectories of neutrons in the reactor, the points of their fission of uranium nuclei, the points of neutron absorption, fission chains and chain reactions are considered from the standpoint of fractal geometry and percolation theory. In the study of the stationary critical operating mode of a nuclear reactor, models of Cayley trees and Laplacian fractals are used. This approach allows us to obtain the neutron multiplication equation and an expression for the critical size of the reactor. Models of irreversible growth and various fractal dimensions are also considered as applied to the evolution of neutrons in a reactor. Prospects for the development of the proposed approach to describing reactors, primarily the kinetics and processes of neutron transfer, are indicated.